Some geometrical properties of convex level sets of minimal graph on 2-dimensional Riemannian manifolds. (January 2016)

• Record Type: Journal Article
• Authors: Wang, Peihe; Zhao, Lingling
• Is Part Of: Nonlinear analysis. Volume 130(2015)
• Page Start: 1
• Page End: 17
• Publication Date: 2016-01
• Subjects: 35J05 -- 53J67; Level sets -- Curvature estimate -- Minimal graph; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.09.021
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: For the minimal graph defined on two dimensional Riemannian manifolds with constant Gauss curvature, we derive a constant rank theorem on the geodesic curvature of its level sets, and an auxiliary function involving the curvature of the level sets will be found to obtain some differential equalities to study the geometrical properties.